Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 5 } { x }$
A)
$\frac { f ( x + h ) - f ( x ) } { h } = 1$
B)
$\frac { f ( x + h ) - f ( x ) } { h } = 5$
C)
$\frac { f ( x + h ) - f ( x ) } { h } = - \frac { 5 } { x ( x + h ) }$
D)
$\frac { f ( x + h ) - f ( x ) } { h } = \frac { 5 } { x + h }$

Question

Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 5 } { x }$
A) 
$\frac { f ( x + h ) - f ( x ) } { h } = 1$
B) 
 $\frac { f ( x + h ) - f ( x ) } { h } = 5$
C) 
$\frac { f ( x + h ) - f ( x ) } { h } = - \frac { 5 } { x ( x + h ) }$
D) 
$\frac { f ( x + h ) - f ( x ) } { h } = \frac { 5 } { x + h }$

Quizplus · Accepted Answer

The difference quotient for $f(x) = \frac{5}{x}$ is calculated as follows: $$\frac{f(x+h)-f(x)}{h} = \frac{\frac{5}{x+h} - \frac{5}{x}}{h} = \frac{5x - 5(x+h)}{hx(x+h)} = -\frac{5h}{hx(x+h)} = -\frac{5}{x(x+h)}$$This simplifies to $-\frac{5}{x(x+h)}$, which matches choice C.

Find the Difference Quotient f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Find the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h }$